Compressor fouling is one of the most prevalent fault modes that contribute to the performance degradation of a gas turbine power plant. Off-line washing is a standard maintenance procedure to recover the fouling degradation, but with washing cost. In this paper, an off-line washing schedule optimization method with a long short-term memory (LSTM) prediction model is proposed to maximize the plant net profit. First, a mechanism model-based gas path analysis method is developed to identify the fouling indications of compressor flow rate degradation (DGC) and compressor efficiency degradation (DEC). Second, a sliding window prediction method based on LSTM is proposed to accurately predict the nonlinear fouling trends. The prediction models are trained and tested by the true trends of the DGC and DEC that are identified from the field data of a real gas turbine power plant. The comparison results prove that the LSTM algorithm outperforms other machine learning algorithms. The mean relative square error of the DGC LSTM model is 9.72 × 10−4, and DEC is 4.08 × 10−4. Finally, a detailed economic model is developed by coupling the fouling prediction model with the gas turbine performance model. On this basis, an optimization method of the washing schedule is developed to maximize the net profit. Two case studies, under full load and field data, are carried out to verify the proposed optimization method. The results show that the washing schedules of the two case studies are much similar, in which three washing tasks with gradually reduced intervals are provided. Furthermore, the comparison results of different schedules show that the proposed optimal schedule has a huge potential in saving the net profit. It can save 3.26 million Yuan compared with the practical schedule adopted by the real power plant.